Horizontal transport in the bouncing ball system with a sawtooth-shaped table

TL;DR

This paper investigates how a bouncing ball on a vertically vibrating sawtooth-shaped table exhibits horizontal transport driven by the table's asymmetry, supported by a simplified probabilistic model that captures the observed behavior.

Contribution

It introduces a simplified probabilistic model to describe asymmetric horizontal transport in a bouncing ball system with a sawtooth table shape.

Findings

Mean horizontal velocity depends on table asymmetry.

Transport direction aligns with gentler slopes.

Simplified model qualitatively reproduces original behavior.

Abstract

The system that consists of a ball bouncing off a sawtooth-shaped table vibrating vertically is considered. The horizontal motion in this system is caused by the table shape, and we plotted the mean horizontal velocity as a function of the asymmetry of the table shape. The ball is transported in the direction which the gentler slopes face. To give a description to the net asymmetric transport, we derived a simplified model using assumptions of high bounce and probabilistic collision to the left or right slopes. The simplified model exhibits a horizontal transport qualitatively similar to that observed in the original model.